Pi-stacking induced NMR spectrum splitting in enantiomerically enriched Ru(II) complexes: evaluation of enantiomeric excess

Several chiral octahedral complexes of the general formula [Ru(bpy)2 (Lig)][PF6]2 (Lig = a ligand that can participate in pi-stacking interactions such as eilatin, isoeilatin, and tpphz) were synthesized in both the racemic and enantiomerically pure/enriched forms. Nonracemic mixtures of enantiomers of all these complexes exhibit splitting of the 1H NMR spectra (NMR nonequivalence); i.e., each spectrum contains a major and a minor set of peaks. The origin of this phenomenon is attributed to a fast equilibrium between monomers and discrete dimers held together by pi-stacking interactions, and it is observed for a wide range of pi-stacking interaction strengths. The NMR spectrum splitting exhibited by these complexes can be exploited for the evaluation of their enantiomeric excess simply from the integral ratio, without addition of chiral shift reagents.     

Theory of the two step enantiomeric purification of 1,3 dimethylallene

An application of a recently proposed [P. Kral et al., Phys. Rev. Lett. 90, 033001 (2003)] two step optical control scenario to the purification of a racemic mixture of 1,3 dimethylallene is presented. Both steps combine adiabatic and diabatic passage phenomena. In the first step, three laser pulses of mutually perpendicular linear polarizations, applied in a "cyclic adiabatic passage" scheme, are shown to be able to distinguish between the L and D enantiomers due to their difference in matter-radiation phase. In the second step, which immediately follows the first, a sequence of pulses is used to convert one enantiomer to its mirror-imaged form. This scenario, which only negligibly populates the first excited electronic state, proves extremely useful for systems such as dimethylallene, which can suffer losses from dissociation and internal conversion upon electronic excitation. We computationally observe conversion of a racemic mixture of dimethylallene to a sample containing approximately 95% of the enantiomer of choice.     

Stable Subnorms II

In this paper we continue our study of stability properties of subnorms on subsets of finite-dimensional, power-associative algebras over the real or the complex numbers.     

Enumeration of substitutional isomers with restrictive mutual positions of ligands: I. Overall counts

We address systematics for the enumeration of substitutional isomers when there is constrained positioning of ligands on a molecular skeleton. One constraint involves ‘restrictive ligands’ where two of the same kind are forbidden to occupy adjacent sites in a molecular skeleton. This may arise because of steric hindrance, or because of groups which in neighbor proximity react to eliminate one. For instance, no pair of –OH groups attach to the same C atom in a molecular skeleton. In another case, malonic acid residues decarboxylate leaving no more than one decarboxylation in each residue. The enumeration with such restrictive ligands may be addressed via a Polya-theoretic cycle index hybridized with the graph-theoretic independence polynomial (when there is just a single such neighbor-excluding ligand and another which is not), while more generally a hybridization with the chromatic polynomial is needed. Another substitional-isomer constraint involves bidentate ligands, with each ligand-part occupying adjacent sites, and possibly also with additional separate unidentate ligands. Here, the set of all pure & mixed such ligand placements is analytically represented by a ‘symmetry-reduced’ matching polynomial (which is a hybrid now of the matching polynomial and Polya’s cycle index). This result gives the generating function for isomer enumeration, taking into account every possible so-restricted assortment of the employed ligands. Here we make such novel hybridizations (for these and other graphtheoretic polynomials) to deal with such oft-encountered chemical problems, which nevertheless transcend typical earlier unconstrained formulizations. Further subsymmetry classification & enumerations, along with examples are considered in a further article.